Trotterization (and its alternative variants) provides a simple approach to digital quantum simulation and is so far the only known approach that can exploit commutativity of the Hamiltonian. Indeed, in the extreme case where all the Hamiltonian terms commute, Trotterization can implement the exact evolution without error. Previous studies have also established commutator analysis of Trotter error for systems with geometrical locality [1]} and Lie-algebraic structures [2]}, as well as certain low-order formulas [3]}, including the first-order Lie-Trotter formula
\({S}_1(t)-e^{-itH}=\int _{0}^{t}\mathrm {d}\tau _1\int _{0}^{\tau _1}\mathrm {d}\tau _2\ e^{-i(t-\tau _1)H}e^{-i\tau _1T}e^{i\tau _2T}\left[iT,iV\right]e^{-i\tau _2T}e^{-i\tau _1V}\) 
